Complete 3. in python assuming 1 and 2 have already been completed

1. Construct a matrix TC of size 240 6 consisting of six temporal sources using three vectors, 1) onsets arrival vector (AV) = [0,20,0,0,0,0], 2) increment vector (IV) = [30,45,60,40,40,40], and 3) duration of ones = [15,20,25,15,20,25]. For instance, you can generate first TC using these three vectors as AV:IV:N-20 =0:30:220 and ones stay active for 15 samples, and N here is 240. This TC is also shown in Figure 1 (left). Mean center each TC by subtracting its mean and standardize each TC by dividing it by its standard deviation. This will make TCs bias free (centered around the origin) and equally important (have unit variance). Plot all TCs as six subplots. Why not normalize (divide by l-2 norm) the TCs instead of standardizing it?

2. A randomly generated correlation matrix (CM) (illustrating uncorrelatedness among all variables) is shown as a sample in Figure 1 (middle). For your case, construct a CM that represents correlation values between 6 variables. Show its plot, and can you tell visually which two TCs are highly correlated? If not, can you tell this from CM?

3. Construct an array tmpSM of size 6(2121) consisting of ones and zeros, by placing ones at these pixels along "vertical,horizontal" direction of the slice i) 02:06,02:06, ii) 02:06,15:19, iii) 08:13,02:06, iv) 08:13,15:19, v) 15:19,02:06, vi) 15:19,15:19. The first SM source is also shown in Figure 1 (right). Plot these SMs in six subplots. Reshape the array tmpSM into a two dimensional matrix and call it SM of size 6 441. Using CM show if these 6 vectored SMs are independent? For our particular case, why standardization of SMs like TCs is not import